3.4 equations of lines. objectives write an equation of a line given information about its graph...
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3.4 Equations of Lines3.4 Equations of Lines
ObjectivesObjectives Write an equation of a line given
information about its graph
Solve problems by writing equations
Equations of LinesEquations of LinesEquations of lines can be written given any of the
following:
The slope and y-intercept
The slope and the coordinates of a point on the line
The coordinates of two points on the line
Equations of LinesEquations of Lines
Slope – Intercept Formy = mx + b
Point – Slope Form
y – y1 = m(x – x1)
Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3.
Answer: The slope-intercept form of the equation of the line is
Slope-intercept form
Example 1:Example 1:
Answer:
Write an equation in point-slope form of the line
whose slope is that contains (–10, 8).
Simplify.
Point-slope form
Example 2:Example 2:
Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0).
Find the slope of the line.
Slope formula
Simplify.
Example 3:Example 3:
Now use the point-slope form and either point to write an equation.
Point-slope form
Add 9 to each side.
Using (4, 9):
Distributive Property
Example 3:Example 3:
Point-slope form
Distributive Property
Using (–2, 0):
Simplify.
Answer:
Example 3:Example 3:
Write an equation in slope-intercept form for a line containing (1, 7) that is perpendicular to the line
the slope
of a line perpendicular to it is 2.
Example 4:Example 4:
Point-slope form
Distributive Property
Add 7 to each side.
Answer:
Example 4:Example 4:
RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Write an equation to represent the total annual cost A for r months of rent.
For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750.
Answer: The total annual cost can be represented by the equation
Slope-intercept form
Example 5a:Example 5a:
RENTAL COSTS An apartment complex charges $525 per month plus a $750 security deposit. Compare this rental cost to a complex which charges a $200 security deposit but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate?
First complex: Second complex:
Simplify.Answer: The first complex offers the better rate: one year
costs $7050 instead of $7400.
Example 5b:Example 5b:
AssignmentAssignment Geometry:
Pg. 148 #16 - 42 evens
Pre-AP Geometry:
Pg. 148 #16 - 44 evens